multiplication-like cordic * (chordic)

Multiplication on early digital computers was typically by sequential approximation
and repetition of addition, progressive cumulation like manual long-multiplication
and long-division implemented in hardware (equipment) for integers, and in software
emulation aided by floating-point addition, -or fully hardware depending on cost,
space, availability, factors-... In the present era it has become replaced by parallel
micro-circuitry.

But by freeing this procedure from fixed multiplier and multiplicand, and speed-ups with
simple fast bit-scaler ("barrel-shifter") and sequential-access memory ("SAM") or other,
more functions can be efficiently calculated:-- Exponentiation; circular-function
sinusoid trigonometric; hypertrigonometric; arithmetic-like
data-compression, ... by algorithm. (Even square-root is such an algorithm.)

Exponentiation could be accomplished by cumulative successive partial multiplications,
Π(1 + d xi) where xi are chosen to simplify the multiplication
to just addition of d=2-i, a bit-scaling (shift) and add or subtract ...
A table of xi is typically n-bits long ... It might be even practical
to build the calculation directly in hardware, even as multiplication was so built--
and useful, as sinusoids are useful in video construction.

The fastest bit-scaler is built on base-8 (near base e² ~7.39),
-requiring the least hardware reduplication and substrate 'realestate'.

* [Author's note: My original article was more inclusive than the ca-1950's
utility, CORDIC CoOrdinate Rotation Digital Computer [algorithm] used for circular
and hyperbolic x-y pair rotations,- but as it was conceptually related as progressive
cumulation of additions, I kept the other's -title- as a subject-reference: believing
it had meant the -subject- of successive narrowing of measure along a cord aka chord,
a progressive binary-search-like calculus-analytic method for measuring nonlinear arcs
by computation, and especially for reducing its error coefficient. (cf Then-new college
subject, my UCSD Department of Applied Physics and Information Sciences APIS,
also-noted Egyption bull, only years after I graduated, became EECS Electronic
Engineering and Computer Sciences; but we'd built computers and interfaces from
small-scale-integration in that era; and SAR Successive Approximation Register was
ordinary technology, decades before calling that, pyramidal.) In my algorithm
discovered-on-demand for myself in college I'd used the process for exponentials,
and later heard and read of the CORDIC describing the same method with paired complex
rotation angle increments chosen similarly to simplify the whole to multiplication
by successively selected single-additions]